Multiscale systems biology and physics of thrombosis under flow

Whole Blood Viscosity and Cerebral Blood Flow in Acute Ischemic Stroke

Existing effective treatments for ischemic stroke restore blood supply to the ischemic region using thrombolysis or mechanical removal of clot. However, it is increasingly recognized that successful removal of occlusive thrombus from the large artery-recanalization, may not always be accompanied by successful restoration of blood flow to the downstream tissues-reperfusion. Ultimately, brain tissue survival depends on cerebral perfusion, and a functioning microcirculation. Because capillary diameter is often equal to or smaller than an erythrocyte, microcirculation is largely dependent on erythrocyte rheological (hemorheological) factors such as whole blood viscosity (WBV). Several studies in the past have demonstrated elevated WBV in stroke compared with healthy controls. Also, elevated WBV has shown to be an independent risk factor for stroke. Elevated WBV leads to endothelial dysfunction, decreases nitric oxide-dependent flow-mediated vasodilation, and promotes hemostatic alterations/thrombosis, all leading to microcirculation sludging. Compromised microcirculation further leads to decreased cerebral perfusion. Hence, modulating WBV through pharmacological agents might be beneficial to improve cerebral perfusion in stroke. This review discusses the effect of elevated WBV on endothelial function, hemostatic alterations, and thrombosis leading to reduced cerebral perfusion in stroke.

The association between admission mean corpuscular volume and preoperative deep venous thrombosis in geriatrics hip fracture: a retrospective study

OBJECTIVE

This study evaluated the association between admission MCV and preoperative deep vein thrombosis (DVT) in geriatric hip fractures.

METHODS

Older adult patients with hip fractures were screened between January 2015 and September 2019. The demographic and clinical characteristics of the patients were collected at the largest trauma center in northwest China. MCV was measured at admission and converted into a categorical variable according to the quartile. Multivariate binary logistic regression and generalized additive model were used to identify the linear and nonlinear association between MCV and preoperative DVT. Analyses were performed using EmpowerStats and the R software.

RESULTS

A total of 1840 patients who met the criteria were finally enrolled and divided into four groups according to their MCV levels. The mean MCV was 93.82 ± 6.49 (80.96 to 105.91 fL), and 587 patients (31.9%) were diagnosed with preoperative DVT. When MCV was a continuous variable, the incidence of preoperative DVT increased with mean corpuscular volume. In the fully adjusted model, admission MCV was positively correlated with the incidence of preoperative DVT (OR: 1.03; 95% CI: 1.01-1.05; P = 0.0013). After excluding the effect of other factors, each additional 1fL of MCV increased the prevalence of preoperative DVT by 1.03 times as a continuous variable.

CONCLUSION

MCV was linearly associated with preoperative DVT in geriatric patients with hip fractures and could be considered a predictor of DVT risk. The MCV may contribute to risk assessment and preventing adverse outcomes in the elderly.

STUDY REGISTRATION

This study is registered on the website of the Chinese Clinical Trial Registry (ChiCTR: ChiCTR2200057323).

Platelet and endothelial cell responses under concurrent shear stress and tensile strain

Thrombosis can lead to significant mortality and morbidity. Both platelets and vascular endothelial cells play significant roles in thrombosis. Platelets' response to blood flow-induced shear stress can vary greatly depending on shear stress magnitude, pattern and shear exposure time. Endothelial cells are also sensitive to the biomechanical environment. Endothelial cell activation and dysfunction can occur under low oscillatory shear stress and low tensile strain. Platelet and endothelial cell interaction can also be affected by mechanical conditions. The goal of this study was to investigate how blood flow-induced shear stress, vascular wall tensile strain, platelet-endothelial cell stress history, and platelet-endothelial cell interaction affect platelet thrombogenicity. Platelets and human coronary artery endothelial cells were pretreated with physiological and pathological shear stress and/or tensile strain separately. The pretreated cells were then put together and exposed to pulsatile shear stress and cyclic tensile strain simultaneously in a shearing-stretching device. Following treatment, platelet thrombin generation rate, platelet and endothelial cell activation, and platelet adhesion to endothelial cells was measured. The results demonstrated that shear stress pretreatment of endothelial cells and platelets caused a significant increase in platelet thrombin generation rate, cell surface phosphatidylserine expression, and adhesion to endothelial cells. Shear stress pretreatment of platelets and endothelial cells attenuated endothelial cell ICAM-1 expression under stenosis conditions, as well as vWF expression under recirculation conditions. These results indicate that platelets are sensitized by prior shearing, while in comparison, the interaction with shear stress-pretreated platelets may reduce endothelial cell sensitivity to pathological shear stress and tensile strain.

Physics-informed neural entangled-ladder network for inhalation impedance of the respiratory system

BACKGROUND AND OBJECTIVES

The use of machine learning methods for modelling bio-systems is becoming prominent which can further improve bio-medical technologies. Physics-informed neural networks (PINNs) can embed the knowledge of physical laws that govern a system during the model training process. PINNs utilise differential equations in the model which traditionally used numerical methods that are computationally complex.

METHODS

We integrate PINNs with an entangled ladder network for modelling respiratory systems by considering a lungs conduction zone to evaluate the respiratory impedance for different initial conditions. We evaluate the respiratory impedance for the inhalation phase of breathing for a symmetric model of the human lungs using entanglement and continued fractions.

RESULTS

We obtain the impedance of the conduction zone of the lungs pulmonary airways using PINNs for nine different combinations of velocity and pressure of inhalation. We compare the results from PINNs with the finite element method using the mean absolute error and root mean square error. The results show that the impedance obtained with PINNs contrasts with the conventional forced oscillation test used for deducing the respiratory impedance. The results show similarity with the impedance plots for different respiratory diseases.

CONCLUSION

We find a decrease in impedance when the velocity of breathing is lowered gradually by 20%. Hence, the methodology can be used to design smart ventilators to the improve flow of breathing.

A novel quantitative method to evaluate the contribution of platelet products to white thrombus formation in reconstituted blood under flow conditions

BACKGROUND AND OBJECTIVES

Currently, the quality of platelet (PLT) products is evaluated using a series of in vitro tests, which only analyse PLTs as an inspection material. However, it would be ideal to assess the physiological functions of PLTs under conditions similar to the sequential blood haemostatic process. In this study, we attempted to establish an in vitro system where the thrombogenicity of PLT products was evaluated in the presence of red blood cells (RBCs) and plasma using a microchamber under constant shear stress (600/s).

MATERIALS AND METHODS

Blood samples were reconstituted by mixing PLT products, standard human plasma (SHP) and standard RBCs. Each component was serially diluted keeping the other two components fixed. The samples were applied onto a flow chamber system (Total Thrombus-formation Analysis System [T-TAS]), and white thrombus formation (WTF) was assessed under large arterial shear conditions.

RESULTS

We observed a good correlation between the PLT numbers in the test samples and WTF. The WTF of samples containing ≦10% SHP was significantly lower than those containing ≧40% SHP, and no difference was observed in WTF among samples containing 40%-100% SHP. WTF significantly declined in the absence of RBCs, whereas no change in WTF was observed in the presence of RBCs, over haematocrit range of 12.5%-50%.

CONCLUSION

The WTF assessed on the T-TAS using reconstituted blood may serve as a new physiological blood thrombus test to quantitatively determine the quality of PLT products.

Effects of the interactions between platelets with other cells in tumor growth and progression

It has been confirmed that platelets play a key role in tumorigenesis. Tumor-activated platelets can recruit blood cells and immune cells to migrate, establish an inflammatory tumor microenvironment at the sites of primary and metastatic tumors. On the other hand, they can also promote the differentiation of mesenchymal cells, which can accelerate the proliferation, genesis and migration of blood vessels. The role of platelets in tumors has been well studied. However, a growing number of studies suggest that interactions between platelets and immune cells (e.g., dendritic cells, natural killer cells, monocytes, and red blood cells) also play an important role in tumorigenesis and tumor development. In this review, we summarize the major cells that are closely associated with platelets and discuss the essential role of the interaction between platelets with these cells in tumorigenesis and tumor development.

COVID-19 and thrombosis: The role of hemodynamics

Severe coronavirus disease 2019 (COVID-19) is characterized by an increased risk of thromboembolic events, a leading cause for adverse outcomes in patients afflicted by the more serious manifestation of the disease. These thromboembolic complications expressed as sepsis-induced coagulopathy, disseminated intravascular coagulation, venous and arterial thromboembolism, pulmonary embolism, microthrombosis, and thrombotic microangiopathy have been observed to affect different organs such as the lungs, heart, kidneys, and brain. Endothelial injury and dysfunction have been identified as the critical pathway towards thrombogenesis, and contributions of other mechanisms such as hypercoagulability, cytokine storm, neutrophils have been studied. However, the contribution of hemodynamic pathways towards thrombosis in severe COVID-19 cases has not been investigated. From the classical theory of Virchow's triad to the contemporary studies on the effect of shear enhanced platelet activation, it is well established that hemodynamics plays a role in the initiation and growth of thrombosis. This article reviews recent studies on COVID-19 related thrombotic events and offers hypotheses on how hemodynamics may be responsible for some of the adverse outcomes observed in severe COVID-19 cases. While thrombogenesis through endothelial injury and the effects of hypercoagulability on thrombosis are briefly addressed, the crux of the discussion is focused on hemodynamic factors such as stasis, turbulent flow, and non-physiological shear stress and their effects on thrombosis. In addition, hemodynamics-dependent venous, arterial, and microvascular thrombosis in COVID-19 cases is discussed. We also propose further investigation of diagnostic and therapeutic options that address the hemodynamics aspects of COVID-19 thrombus formation to assess their potential in patient care.

Continuum modeling of thrombus formation and growth under different shear rates

Obstruction of blood flow due to thrombosis is a major cause of ischemic stroke, myocardial infarction, and in severe cases, mortality. In particular, in blood wetting medical devices, thrombosis is a common reason for failure. The prediction of thrombosis by understanding signaling pathways using computational models, lead to identify the risk of thrombus formation in blood-contacting devices and design improvements. In this study, a mathematical model of thrombus formation and growth is presented. A biochemical model of platelet activation and aggregation is developed to predict thrombus size and shape at the site of vascular injury. Computational fluid dynamics using the finite volume method is employed to compute the velocity and pressure fields which are influenced by the growing thrombi. The passive transport of platelets, agonists, the platelet activation kinetics, their adhesion to the growing thrombi and embolization of platelets are solved by a fully coupled set of convection-diffusion-reaction equations. The thrombogenic surface representing blood-contacting material or injured blood vessel was incorporated into the model as a surface flux boundary condition to initiate thrombus formation. The blood is considered as a Newtonian fluid, while the thrombus is treated as a porous medium. The results are compared with in vitro experiments of a microfluidic chamber at an initial inlet venous shear rate of 200s^-1 using a pressure-inlet boundary condition. The thrombus development due to agonist concentrations and change in the shear rate as well as thromboembolism for this benchmark problem is successfully computed. Furthermore, to extend the current model to a physiologically relevant configuration, thrombus formation in a blood tube is simulated. Two different heterogeneous reaction rates for platelet aggregation are used to simulate thrombus growth under a constant inlet flow rate. The findings show that the thrombus shape can be substantially altered by the hemodynamic conditions, increase in the shear rate and due to the combined effects of shear induced platelet activation and the heterogeneous reaction rates. It is also concluded that the model is able to predict thrombus formation in different physiological and pathological hemodynamics.

Microstructure aware modeling of biochemical transport in arterial blood clots

Flow-mediated transport of biochemical species is central to thrombotic phenomena. Comprehensive three-dimensional modeling of flow-mediated transport around realistic macroscale thrombi poses challenges owing to their arbitrary heterogeneous microstructure. Here, we develop a microstructure aware model for species transport within and around a macroscale thrombus by devising a custom preconditioned fictitious domain formulation for thrombus-hemodynamics interactions, and coupling it with a fictitious domain advection-diffusion formulation for transport. Microstructural heterogeneities are accounted through a hybrid discrete particle-continuum approach for the thrombus interior. We present systematic numerical investigations on unsteady arterial flow within and around a three-dimensional macroscale thrombus; demonstrate the formation of coherent flow structures around the thrombus which organize advective transport; illustrate the role of the permeation processes at the thrombus boundary and subsequent intra-thrombus transport; and characterize species transport from bulk flow to the thrombus boundary and vice versa.

A 1D-3D Hybrid Model of Patient-Specific Coronary Hemodynamics

PURPOSE

Coronary flow is affected by evolving events such as atherosclerotic plaque formation, rupture, and thrombosis, resulting in myocardial ischemia and infarction. Highly resolved 3D hemodynamic data at the stenosis is essential to model shear-sensitive thrombotic events in coronary artery disease.

METHODS

We developed a hybrid 1D-3D simulation framework to compute patient-specific coronary hemodynamics efficiently. A 1D model of the coronary flow is coupled to an image-based 3D model of the region of interest. This framework affords the advantages of reduced-order modeling, decreasing the global computational cost, without sacrificing the accuracy of the quantities of interest.

RESULTS

We validated our 1D-3D model against full 3D coronary simulations in healthy and diseased conditions. Our results showed good agreement between the 3D and the 1D-3D models while reducing the computational cost by 40-fold compared to the 3D simulation. The 1D-3D model predicted left/right coronary flow distribution within 3% and provided an accurate estimation of fractional flow reserve and wall shear stress distribution at the stenosis comparable to the 3D simulation.

CONCLUSION

Savings in computational cost may be significant in situations with changing geometry, such as growing thrombosis. Also, this approach would allow quantifying the time-dependent effect of thrombotic growth and occlusion on the global coronary circulation.

Statistical Learning from Single-Molecule Experiments: Support Vector Machines and Expectation-Maximization Approaches to Understanding Protein Unfolding Data

Single-molecule force spectroscopy has become a powerful tool for the exploration of dynamic processes that involve proteins; yet, meaningful interpretation of the experimental data remains challenging. Owing to low signal-to-noise ratio, experimental force-extension spectra contain force signals due to nonspecific interactions, tip or substrate detachment, and protein desorption. Unravelling of complex protein structures results in the unfolding transitions of different types. Here, we test the performance of Support Vector Machines (SVM) and Expectation Maximization (EM) approaches in statistical learning from dynamic force experiments. When the output from molecular modeling in silico (or other studies) is used as a training set, SVM and EM can be applied to understand the unfolding force data. The maximal margin or maximum likelihood classifier can be used to separate experimental test observations into the unfolding transitions of different types, and EM optimization can then be utilized to resolve the statistics of unfolding forces: weights, average forces, and standard deviations. We designed an EM-based approach, which can be directly applied to the experimental data without data classification and division into training and test observations. This approach performs well even when the sample size is small and when the unfolding transitions are characterized by overlapping force ranges.

Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood

A pathologically formed blood clot or thrombus is central to major cardiovascular diseases like heart attack and stroke. Detailed quantitative evaluation of flow and flow-mediated transport processes in the thrombus neighborhood within large artery hemodynamics is crucial for understanding disease progression and assessing treatment efficacy. This, however, remains a challenging task owing to the complexity of pulsatile viscous flow interactions with arbitrary shape and heterogeneous microstructure of realistic thrombi. Here, we address this challenge by conducting a systematic parametric simulation-based study on characterizing unsteady hemodynamics and flow-mediated transport in the neighborhood of an arterial thrombus. We use a hybrid particle-continuum-based finite element approach to handle arbitrary thrombus shape and microstructural variations. Results from a cohort of 50 different unsteady flow scenarios are presented, including unsteady vortical structures, pressure gradient across the thrombus boundary, finite time Lyapunov exponents, and dynamic coherent structures that organize advective transport. We clearly illustrate the combined influence of three key parameters-thrombus shape, microstructure, and extent of wall disease-in terms of: (a) determining hemodynamic features in the thrombus neighborhood and (b) governing the balance between advection, permeation, and diffusion to regulate transport processes in the thrombus neighborhood.

Hematotoxic Snakebite Victim with Trauma: The Role of Guided Transfusion, Rotational Thromboelastometry, and Tranexamic Acid

Hematotoxic snake bite is a leading cause of mortality in South India. However, it is rare for the emergency physician to encounter a patient with trauma associated with snakebite. Management of such a patient differs substantially from the routine management of either a trauma patient or a snakebite victim. A 59-y-old man was bitten by a snake, after which he lost consciousness, fell, and sustained facial trauma. He was rushed to the emergency department within 30 min and was discovered to have ongoing oromaxillofacial bleeding. His respiratory distress and gasping respirations warranted orotracheal intubation and ventilation. He was treated with anti-snake venom and underwent viscoelastometry-guided transfusion to correct coagulopathy. Hemostasis was achieved after administration of tranexamic acid and bilateral posterior nasal packing. Imaging studies revealed craniomaxillofacial trauma with intracranial hemorrhage. He underwent a delayed mandibular repair. Judicious, guided fluid management, adequate nutrition, and prompt weaning off the ventilator allowed early discharge of the patient from the hospital. The minimal weakness present in his left lower limb at the time of discharge had improved by the time of follow-up. This report shows the utility of early and rapid anti-snake venom in envenomated victims with coagulopathy. The role of cryoprecipitate, tranexamic acid, and viscoelastometric testing needs further exploration in specific hematotoxic snakebites.

Computationally Driven Discovery in Coagulation

Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).

Spherization of red blood cells and platelet margination in COPD patients

Red blood cells (RBCs) in pathological situations undergo biochemical and conformational changes, leading to alterations in rheology involved in cardiovascular events. The shape of RBCs in volunteers and stable and exacerbated chronic obstructive pulmonary disease (COPD) patients was analyzed. The effects of RBC spherization on platelet transport (displacement in the flow field caused by their interaction with RBCs) were studied in vitro and by numerical simulations. RBC spherization was observed in COPD patients compared with volunteers. In in vitro experiments at a shear rate of 100 s^-1 , treatment of RBCs with neuraminidase induced greater sphericity, which mainly affected platelet aggregates without changing aggregate size. At 400 s^-1 , neuraminidase treatment changes both the size of the aggregates and the number of platelet aggregates. Numerical simulations indicated that RBC spherization induces an increase of the platelet mean square displacement, which is traditionally linked to the platelet diffusion coefficient. RBCs of COPD patients are more spherical than healthy volunteers. Experimentally, RBC spherization induces increased platelet transport to the wall. Additional studies are needed to understand the link between the effect of RBCs on platelet transport and the increased cardiovascular events observed in COPD patients.

Revealing the molecular origins of fibrin's elastomeric properties by in situ X-ray scattering

Fibrin is an elastomeric protein forming highly extensible fiber networks that provide the scaffold of blood clots. Here we reveal the molecular mechanisms that explain the large extensibility of fibrin networks by performing in situ small angle X-ray scattering measurements while applying a shear deformation. We simultaneously measure shear-induced alignment of the fibers and changes in their axially ordered molecular packing structure. We show that fibrin networks exhibit distinct structural responses that set in consecutively as the shear strain is increased. They exhibit an entropic response at small strains (<5%), followed by progressive fiber alignment (>25% strain) and finally changes in the fiber packing structure at high strain (>100%). Stretching reduces the fiber packing order and slightly increases the axial periodicity, indicative of molecular unfolding. However, the axial periodicity changes only by 0.7%, much less than the 80% length increase of the fibers, suggesting that fiber elongation mainly stems from uncoiling of the natively disordered αC-peptide linkers that laterally bond the molecules. Upon removal of the load, the network structure returns to the original isotropic state, but the fiber structure becomes more ordered and adopts a smaller packing periodicity compared to the original state. We conclude that the hierarchical packing structure of fibrin fibers, with built-in disorder, makes the fibers extensible and allows for mechanical annealing. Our results provide a basis for interpreting the molecular basis of haemostatic and thrombotic disorders associated with clotting and provide inspiration to design resilient bio-mimicking materials. STATEMENT OF SIGNIFICANCE: Fibrin provides structural integrity to blood clots and is also widely used as a scaffold for tissue engineering. To fulfill their biological functions, fibrin networks have to be simultaneously compliant like skin and resilient against rupture. Here, we unravel the structural origin underlying this remarkable mechanical behaviour. To this end, we performed in situ measurements of fibrin structure across multiple length scales by combining X-ray scattering with shear rheology. Our findings show that fibrin sustains large strains by undergoing a sequence of structural changes on different scales with increasing strain levels. This demonstrates new mechanistic aspects of an important biomaterial's structure and its mechanical function, and serves as an example in the design of biomimicking materials.

Red blood cells: the forgotten player in hemostasis and thrombosis

New evidence has stirred up a long-standing but undeservedly forgotten interest in the role of erythrocytes, or red blood cells (RBCs), in blood clotting and its disorders. This review summarizes the most recent research that describes the involvement of RBCs in hemostasis and thrombosis. There are both quantitative and qualitative changes in RBCs that affect bleeding and thrombosis, as well as interactions of RBCs with cellular and molecular components of the hemostatic system. The changes in RBCs that affect hemostasis and thrombosis include RBC counts or hematocrit (modulating blood rheology through viscosity) and qualitative changes, such as deformability, aggregation, expression of adhesive proteins and phosphatidylserine, release of extracellular microvesicles, and hemolysis. The pathogenic mechanisms implicated in thrombotic and hemorrhagic risk include variable adherence of RBCs to the vessel wall, which depends on the functional state of RBCs and/or endothelium, modulation of platelet reactivity and platelet margination, alterations of fibrin structure and reduced susceptibility to fibrinolysis, modulation of nitric oxide availability, and the levels of von Willebrand factor and factor VIII in blood related to the ABO blood group system. RBCs are involved in platelet-driven contraction of clots and thrombi that results in formation of a tightly packed array of polyhedral erythrocytes, or polyhedrocytes, which comprises a nearly impermeable barrier that is important for hemostasis and wound healing. The revisited notion of the importance of RBCs is largely based on clinical and experimental associations between RBCs and thrombosis or bleeding, implying that RBCs are a prospective therapeutic target in hemostatic and thrombotic disorders.

Model predictions of deformation, embolization and permeability of partially obstructive blood clots under variable shear flow

Thromboembolism, one of the leading causes of morbidity and mortality worldwide, is characterized by formation of obstructive intravascular clots (thrombi) and their mechanical breakage (embolization). A novel two-dimensional multi-phase computational model is introduced that describes active interactions between the main components of the clot, including platelets and fibrin, to study the impact of various physiologically relevant blood shear flow conditions on deformation and embolization of a partially obstructive clot with variable permeability. Simulations provide new insights into mechanisms underlying clot stability and embolization that cannot be studied experimentally at this time. In particular, model simulations, calibrated using experimental intravital imaging of an established arteriolar clot, show that flow-induced changes in size, shape and internal structure of the clot are largely determined by two shear-dependent mechanisms: reversible attachment of platelets to the exterior of the clot and removal of large clot pieces. Model simulations predict that blood clots with higher permeability are more prone to embolization with enhanced disintegration under increasing shear rate. In contrast, less permeable clots are more resistant to rupture due to shear rate-dependent clot stiffening originating from enhanced platelet adhesion and aggregation. These results can be used in future to predict risk of thromboembolism based on the data about composition, permeability and deformability of a clot under specific local haemodynamic conditions.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Platelets from flowing blood attach to the inflammatory chemokine CXCL16 expressed in the endothelium of the human vessel wall

Endothelial chemokine CXC motif ligand 16 (CXCL16) expression is associated with atherosclerosis, while platelets, particularly those attaching to atherosclerotic plaque, contribute to all stages of athero-sclerotic disease. This investigation was designed to examine the role of CXCL16 in capturing platelets from flowing blood. CXCL16 was expressed in human atherosclerotic plaques, and lesion severity in human carotid endarterectomy specimens was positively correlated with CXCL16 levels. CXCL16 expression in plaques was co-localised with platelets deposited to the endothelium. Immobilised CXCL16 promoted CXCR6-dependent platelet adhesion to the human vessel wall, endothelial cells and von Willebrand factor during physiologic flow. At low shear, immobilised CXCL16 captured platelets from flowing blood. It also induced irreversible platelet aggregation and a rise in intra-platelet calcium levels. These results demonstrate that endothelial CXCL16’s action on platelets is not only limited to platelet activation, but that immobilised CXCL16 also acts as a potent novel platelet adhesion ligand, inducing platelet adhesion to the human vessel wall.

Primary Human Lung Alveolus-on-a-chip Model of Intravascular Thrombosis for Assessment of Therapeutics

Pulmonary thrombosis is a significant cause of patient mortality; however, there are no effective in vitro models of thrombi formation in human lung microvessels that could also assess therapeutics and toxicology of antithrombotic drugs. Here, we show that a microfluidic lung alveolus-on-a-chip lined by human primary alveolar epithelium interfaced with endothelium and cultured under flowing whole blood can be used to perform quantitative analysis of organ-level contributions to inflammation-induced thrombosis. This microfluidic chip recapitulates in vivo responses, including platelet-endothelial dynamics and revealed that lipopolysaccharide (LPS) endotoxin indirectly stimulates intravascular thrombosis by activating the alveolar epithelium, rather than acting directly on endothelium. This model is also used to analyze inhibition of endothelial activation and thrombosis due to a protease activated receptor-1 (PAR-1) antagonist, demonstrating its ability to dissect complex responses and identify antithrombotic therapeutics. Thus, this methodology offers a new approach to study human pathophysiology of pulmonary thrombosis and advance drug development.

Role of red blood cells in haemostasis and thrombosis

In contrast to an obsolete notion that erythrocytes, or red blood cells (RBCs), play a passive and minor role in hemostasis and thrombosis, over the past decades there has been increasing evidence that RBCs have biologically and clinically important functions in blood clotting and its disorders. This review summarizes the main mechanisms that underlie the involvement of RBCs in hemostasis and thrombosis in vivo, such as rheological effects on blood viscosity and platelet margination, aggregation and deformability of RBCs; direct adhesion and indirect biochemical interactions with endothelial cells and platelets, etc. The ability of stored and pathologically altered RBCs to generate thrombin through exposure of phosphatidylserine has been emphasized. The procoagulant and prothrombotic potential of RBC-derived microparticles transfused with stored RBCs or formed in various pathological conditions associated with hemolysis has been described along with prothrombotic effects of free hemoglobin and heme. Binding of fibrinogen or fibrin to RBCs may influence their effects on fibrin network structure, clot mechanical properties, and fibrinolytic resistance. Recent data on platelet-driven clot contraction show that RBCs compressed by platelets pulling on fibrin form a tightly packed array of polyhedral erythrocytes, or polyhedrocytes, which comprises a nearly impermeable barrier important for hemostasis and wound healing. RBCs may perform dual roles, both helping to stem bleeding but at the same time contributing to thrombosis in a variety of ways.

Fibrin Formation, Structure and Properties

Fibrinogen and fibrin are essential for hemostasis and are major factors in thrombosis, wound healing, and several other biological functions and pathological conditions. The X-ray crystallographic structure of major parts of fibrin(ogen), together with computational reconstructions of missing portions and numerous biochemical and biophysical studies, have provided a wealth of data to interpret molecular mechanisms of fibrin formation, its organization, and properties. On cleavage of fibrinopeptides by thrombin, fibrinogen is converted to fibrin monomers, which interact via knobs exposed by fibrinopeptide removal in the central region, with holes always exposed at the ends of the molecules. The resulting half-staggered, double-stranded oligomers lengthen into protofibrils, which aggregate laterally to make fibers, which then branch to yield a three-dimensional network. Much is now known about the structural origins of clot mechanical properties, including changes in fiber orientation, stretching and buckling, and forced unfolding of molecular domains. Studies of congenital fibrinogen variants and post-translational modifications have increased our understanding of the structure and functions of fibrin(ogen). The fibrinolytic system, with the zymogen plasminogen binding to fibrin together with tissue-type plasminogen activator to promote activation to the active proteolytic enzyme, plasmin, results in digestion of fibrin at specific lysine residues. In spite of a great increase in our knowledge of all these interconnected processes, much about the molecular mechanisms of the biological functions of fibrin(ogen) remains unknown, including some basic aspects of clotting, fibrinolysis, and molecular origins of fibrin mechanical properties. Even less is known concerning more complex (patho)physiological implications of fibrinogen and fibrin.

Dynamics of blood flow and thrombus formation in a multi-bypass microfluidic ladder network

The reaction dynamics of a complex mixture of cells and proteins, such as blood, in branched circulatory networks within the human microvasculature or extravascular therapeutic devices such as extracorporeal oxygenation machine (ECMO) remains ill-defined. In this report we utilize a multi-bypass microfluidics ladder network design with dimensions mimicking venules to study patterns of blood platelet aggregation and fibrin formation under complex shear. Complex blood fluid dynamics within multi-bypass networks under flow were modeled using COMSOL. Red blood cells and platelets were assumed to be non-interacting spherical particles transported by the bulk fluid flow, and convection of the activated coagulation factor II, thrombin, was assumed to be governed by mass transfer. This model served as the basis for predicting formation of local shear rate gradients, stagnation points and recirculation zones as dictated by the bypass geometry. Based on the insights from these models, we were able to predict the patterns of blood clot formation at specific locations in the device. Our experimental data was then used to adjust the model to account for the dynamical presence of thrombus formation in the biorheology of blood flow. The model predictions were then compared to results from experiments using recalcified whole human blood. Microfluidic devices were coated with the extracellular matrix protein, fibrillar collagen, and the initiator of the extrinsic pathway of coagulation, tissue factor. Blood was perfused through the devices at a flow rate of 2 µL/min, translating to physiologically relevant initial shear rates of 300 and 700 s^-1 for main channels and bypasses, respectively. Using fluorescent and light microscopy, we observed distinct flow and thrombus formation patterns near channel intersections at bypass points, within recirculation zones and at stagnation points. Findings from this proof-of-principle ladder network model suggest a specific correlation between microvascular geometry and thrombus formation dynamics under shear. This model holds potential for use as an integrative approach to identify regions susceptible to intravascular thrombus formation within the microvasculature as well as extravascular devices such as ECMO.

Fibrin mechanical properties and their structural origins

Fibrin is a protein polymer that is essential for hemostasis and thrombosis, wound healing, and several other biological functions and pathological conditions that involve extracellular matrix. In addition to molecular and cellular interactions, fibrin mechanics has been recently shown to underlie clot behavior in the highly dynamic intra- and extravascular environments. Fibrin has both elastic and viscous properties. Perhaps the most remarkable rheological feature of the fibrin network is an extremely high elasticity and stability despite very low protein content. Another important mechanical property that is common to many filamentous protein polymers but not other polymers is stiffening occurring in response to shear, tension, or compression. New data has begun to provide a structural basis for the unique mechanical behavior of fibrin that originates from its complex multi-scale hierarchical structure. The mechanical behavior of the whole fibrin gel is governed largely by the properties of single fibers and their ensembles, including changes in fiber orientation, stretching, bending, and buckling. The properties of individual fibrin fibers are determined by the number and packing arrangements of double-stranded half-staggered protofibrils, which still remain poorly understood. It has also been proposed that forced unfolding of sub-molecular structures, including elongation of flexible and relatively unstructured portions of fibrin molecules, can contribute to fibrin deformations. In spite of a great increase in our knowledge of the structural mechanics of fibrin, much about the mechanisms of fibrin's biological functions remains unknown. Fibrin deformability is not only an essential part of the biomechanics of hemostasis and thrombosis, but also a rapidly developing field of bioengineering that uses fibrin as a versatile biomaterial with exceptional and tunable biochemical and mechanical properties.

Regulation of Early Steps of GPVI Signal Transduction by Phosphatases: A Systems Biology Approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation.

A comprehensive study on different modelling approaches to predict platelet deposition rates in a perfusion chamber

Thrombus formation is a multiscale phenomenon triggered by platelet deposition over a protrombotic surface (eg. a ruptured atherosclerotic plaque). Despite the medical urgency for computational tools that aid in the early diagnosis of thrombotic events, the integration of computational models of thrombus formation at different scales requires a comprehensive understanding of the role and limitation of each modelling approach. We propose three different modelling approaches to predict platelet deposition. Specifically, we consider measurements of platelet deposition under blood flow conditions in a perfusion chamber for different time periods (3, 5, 10, 20 and 30 minutes) at shear rates of 212 s⁻¹, 1390 s⁻¹ and 1690 s⁻¹. Our modelling approaches are: i) a model based on the mass-transfer boundary layer theory; ii) a machine-learning approach; and iii) a phenomenological model. The results indicate that the three approaches on average have median errors of 21%, 20.7% and 14.2%, respectively. Our study demonstrates the feasibility of using an empirical data set as a proxy for a real-patient scenario in which practitioners have accumulated data on a given number of patients and want to obtain a diagnosis for a new patient about whom they only have the current observation of a certain number of variables.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

Platelet dynamics in three-dimensional simulation of whole blood

A high-fidelity computational model using a 3D immersed boundary method is used to study platelet dynamics in whole blood. We focus on the 3D effects of the platelet-red blood cell (RBC) interaction on platelet margination and near-wall dynamics in a shear flow. We find that the RBC distribution in whole blood becomes naturally anisotropic and creates local clusters and cavities. A platelet can enter a cavity and use it as an express lane for a fast margination toward the wall. Once near the wall, the 3D nature of the platelet-RBC interaction results in a significant platelet movement in the transverse (vorticity) direction and leads to anisotropic platelet diffusion within the RBC-depleted zone or cell-free layer (CFL). We find that the anisotropy in platelet motion further leads to the formation of platelet clusters, even in the absence of any platelet-platelet adhesion. The transverse motion, and the size and number of the platelet clusters are observed to increase with decreasing CFL thickness. The 3D nature of the platelet-RBC collision also induces fluctuations in off-shear plane orientation and, hence, a rotational diffusion of the platelets. Although most marginated platelets are observed to tumble just outside the RBC-rich zone, platelets further inside the CFL are observed to flow with an intermittent dynamics that alters between sliding and tumbling, as a result of the off-shear plane rotational diffusion, bringing them even closer to the wall. To our knowledge, these new findings are based on the fundamentally 3D nature of the platelet-RBC interaction, and they underscore the importance of using cellular-scale 3D models of whole blood to understand platelet margination and near-wall platelet dynamics.

Fluid Mechanics of Blood Clot Formation

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

A haemodynamic predictor of intraluminal thrombus formation in abdominal aortic aneurysms

Intraluminal thrombus (ILT) is present in over 75% of all abdominal aortic aneurysms (AAAs) and probably contributes to the complex biomechanics and pathobiology of these lesions. A reliable predictor of thrombus formation in enlarging lesions could thereby aid clinicians in treatment planning. The primary goal of this work was to identify a new phenomenological metric having clinical utility that is motivated by the hypothesis that two basic haemodynamic features must coincide spatially and temporally to promote the formation of a thrombus on an intact endothelium—platelets must be activated within a shear flow and then be presented to a susceptible endothelium. Towards this end, we propose a new thrombus formation potential (TFP) that combines information on the flow-induced shear history experienced by blood-borne particles that come in close proximity to the endothelium with information on both the time-averaged wall shear stress (WSS) and the oscillatory shear index (OSI) that locally affect the endothelial mechanobiology. To illustrate the possible utility of this new metric, we show computational results for 10 carotid arteries from five patients where regions of low WSS and high OSI tend not to be presented with activated platelets (i.e. they have a low TFP), consistent with the thrombo-resistance of the healthy carotid despite its complex haemodynamics. Conversely, we show results for three patients that high TFP co-localizes with regions of observed thin thrombus in AAAs, which contrasts with findings of low TFP for the abdominal aorta of three healthy subjects. We submit that these promising results suggest the need for further consideration of the TFP, or a similar combined metric, as a potentially useful clinical predictor of the possible formation of ILT in AAAs.

A continuum model for platelet plug formation, growth and deformation

A numerical framework for modelling platelet plug dynamics is presented in this work. It consists of an extension of a biochemical and plug growth model with a solid mechanics model for the plug coupled with a fluid-structure interaction model for the blood flow-plug system. The platelet plug is treated as a neo-Hookean elastic solid, of which the implementation is based on an updated Lagrangian approach. The framework is applied to different haemodynamic configurations coupled with different shear moduli of the plug. Results about plug growth, shape and size, as well as the stress distribution, are shown. Based on the simulations performed, we conclude that the deformability of the platelet plug is essential for its growth.

Tuneable resolution as a systems biology approach for multi-scale, multi-compartment computational models

The use of multi-scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi-scale models span a range of spatial and/or temporal scales and can encompass multi-compartment (e.g., multi-organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet-lab. Wet-lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi-scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi:10.1002/wsbm.1270

How to cite this article:WIREs Syst Biol Med 2014, 6:289–309. doi:10.1002/wsbm.1270

Systems biology of platelet-vessel wall interactions

Platelets are small, anucleated cells that participate in primary hemostasis by forming a hemostatic plug at the site of a blood vessel's breach, preventing blood loss. However, hemostatic events can lead to excessive thrombosis, resulting in life-threatening strokes, emboli, or infarction. Development of multi-scale models coupling processes at several scales and running predictive model simulations on powerful computer clusters can help interdisciplinary groups of researchers to suggest and test new patient-specific treatment strategies.

Biochemomechanics of intraluminal thrombus in abdominal aortic aneurysms

Most computational models of abdominal aortic aneurysms address either the hemodynamics within the lesion or the mechanics of the wall. More recently, however, some models have appropriately begun to account for the evolving mechanics of the wall in response to the changing hemodynamic loads. Collectively, this large body of work has provided tremendous insight into this life-threatening condition and has provided important guidance for current research. Nevertheless, there has yet to be a comprehensive model that addresses the mechanobiology, biochemistry, and biomechanics of thrombus-laden abdominal aortic aneurysms. That is, there is a pressing need to include effects of the hemodynamics on both the development of the nearly ubiquitous intraluminal thrombus and the evolving mechanics of the wall, which depends in part on biochemical effects of the adjacent thrombus. Indeed, there is increasing evidence that intraluminal thrombus in abdominal aortic aneurysms is biologically active and should not be treated as homogeneous inert material. In this review paper, we bring together diverse findings from the literature to encourage next generation models that account for the biochemomechanics of growth and remodeling in patient-specific, thrombus-laden abdominal aortic aneurysms.

Hydrodynamic interaction between a platelet and an erythrocyte: effect of erythrocyte deformability, dynamics, and wall proximity

We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a front-tracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.

Numerical and experimental evaluation of platelet deposition to collagen coated surface at low shear rates

Platelet deposition to collagen-coated surface under low shear conditions was investigated using an experimental model. The flow chamber was created by combining a stationary and a rotational glass plates spaced 50 μm apart. Blood filled into this space was subjected to a simple Couette flow. Both glass plates were covered with albumin to render them anti-thrombogenic. However, one spot 1×1 mm in size was covered with collagen. This spot was where the platelets deposited. The device was mounted on an inverted microscope and the platelet deposition was recorded. Platelets were dyed to render them fluorescent. The blood used was human blood from healthy volunteers. It was subjected to a range of low shear rates (below 7001/s) to find out how they act on platelet deposition. The results show a characteristic curve with elevated platelet deposition in the range of 1501/s. For the interpretation of these results a numerical model was developed. It applies the Monte Carlo method to model a random walk of platelets. This diffusive motion was superimposed on the convective motion by the Couette flow. A satisfactory match to the experimental data was achieved.